[3.6] Copy Property Does Not Work

### Tested versions

v3.6.stable.official [de2f0f147]

### System information

w11 64

### Issue description

When clicking "Copy Property," nothing is copied, and pasting still uses the previously stored content in the clipboard.

https://github.com/user-attachments/assets/b9aa25d3-f810-413b-8680-55a26b672692

### Steps to reproduce

See the video.

### Minimal reproduction project (MRP)

Any project.

Reproduce the issue in Godot v3.6.stable.official on Windows 11 using any project, following the reported Copy Property action and checking whether the clipboard changes. Trace the editor path handling Copy Property, then verify that pasting uses the newly copied value rather than the previous clipboard contents.

Written by the indexing model from the issue text.